Dynamic analysis of a spatial diffusion rumor propagation model with delay

In this paper, we study the dynamics of a delayed reaction-diffusion rumor model with government control. By using the theory of partial functional differential equations, a Hopf bifurcation of the proposed system with delay as the bifurcation parameter is investigated. It reveals that the discrete time delay has a destabilizing effect in the rumor dynamics, and the phenomenon of Hopf bifurcation occurs as the delay increases through a certain threshold. Then by numerical simulations the impact of government control is explored. It is found that government control has strong effects on the dynamics of the model.

[1]  Jingjing Cheng,et al.  SIHR rumor spreading model in social networks , 2012 .

[2]  Jie Zhou,et al.  Influence of network structure on rumor propagation , 2007 .

[3]  On the existence of impulsive neutral evolution differential inclusions with infinite delay , 2015 .

[4]  Wanlin Xie,et al.  A rumor spreading model with variable forgetting rate , 2013 .

[5]  C. V. Pao,et al.  Convergence of solutions of reaction-diffusion systems with time delays , 2002 .

[6]  Peiqing Huang,et al.  Analyzing the Dynamics of a Rumor Transmission Model with Incubation , 2012 .

[7]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Katsuhide Warashina,et al.  A rumor transmission model with various contact interactions. , 2008, Journal of theoretical biology.

[9]  R. Descartes,et al.  The Philosophical Writings of Descartes: Index , 1985 .

[10]  C. V. Pao,et al.  On nonlinear reaction-diffusion systems , 1982 .

[11]  Haiyan Wang,et al.  On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations , 1995 .

[12]  Wei Huang,et al.  Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal , 2011 .

[13]  Huo Liang-a.  Study on Rumor Propagation Models Based on Dynamical System Theory , 2013 .

[14]  Liang’an Huo,et al.  Optimal control of a rumor propagation model with latent period in emergency event , 2015, Advances in Difference Equations.

[15]  Ying Zhang,et al.  An information diffusion model based on retweeting mechanism for online social media , 2012 .

[16]  Xiaohua Jia,et al.  Characterizing Information Diffusion in Online Social Networks with Linear Diffusive Model , 2013, 2013 IEEE 33rd International Conference on Distributed Computing Systems.

[17]  J. Cottingham,et al.  The Philosophical Writings of Descartes: Volume 1 , 1985 .

[18]  Ding Zhang,et al.  The impact of authorities’ media and rumor dissemination on the evolution of emergency , 2012 .

[19]  Alessandro Vespignani,et al.  Efficiency and reliability of epidemic data dissemination in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  C. V. Pao,et al.  Dynamics of Nonlinear Parabolic Systems with Time Delays , 1996 .

[21]  Rui Xu,et al.  Global stability of a SIR epidemic model with nonlinear incidence rate and time delay , 2009 .

[22]  Chia-Ven Pao,et al.  Nonlinear parabolic and elliptic equations , 1993 .

[23]  Yi Zhang,et al.  Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion , 2011, PloS one.

[24]  Xing Fang,et al.  An interplay model for authorities’ actions and rumor spreading in emergency event , 2011 .